Fundamentals of General Insurance Actuarial Analysis

By Jacqueline Friedland · Society of Actuaries · 2022

Study guides: Exam GI-101, Exam GI-201, Exam GI-301

A Society of Actuaries textbook by Jacqueline Friedland, in its second edition (2022), on general insurance actuarial analysis. It is built around the actuarial control cycle (define the problem, design a solution, monitor results) and aims to be a practical guide rather than a theoretical discourse, with examples embedded in the text and in case studies in the appendices. Its parts run from key concepts and data preparation through methods for estimating ultimate claims, financial reporting, trending, ratemaking and monitoring results.

On the syllabus

• Exam GI-101 — Chapter 2 (1a-p); Part 2: Key Concepts, excluding Chapter 10 (1a-p); Part 3: Preparing the Data, excluding 12.6.4 and 12.6.6 (2a-f); Appendices A through C and F, excluding Sections A.3.6 and A.5 (2a-f, 3a-m, 5a-e, 6a-h, 7a-f); Part 4: Basic Methods for Estimating Ultimate Claims, excluding 15.8, 16.6, 16.7, 17.8, 18.8, 19.6, 20.6, 21.3.5 and 21.3.6 (3a-m); Chapter 23, excluding section 23.4 (4a-c); Part 6: Trending Procedures (5a-e); Part 7: Ratemaking, Chapters 30 through 32 (6a-h).
• Exam GI-201 — Ch. 29: Manual Ratemaking (1d); Ch. 28: Rate Regulation (2a); Ch. 24: Claim Liabilities (5d).
• Exam GI-301 — Appendix G: Development Analysis for Excess Limits and Layers (2a, 2b); Ch. 25: Premium Liabilities (3a, 3b); Appendix A: Dentist Insurer, section A.3.6 (3a, 3b); Appendix D: ABC Manufacturing Company/ABCMC Captive, section D.6 (3a, 3b); Ch. 37: Monitoring Results (5a, 5b); Appendix E: Public Entity Self-Insurance Pool, sections E.3.1 and E.3.2 (5a, 5b); Ch. 33: Basic Risk Classification (6a, 6b); Ch. 34: Actuarial Pricing for Deductibles and Increased Limits (6c); Appendix D, section D.4 (6c); Appendix E, sections E.3.4 and E.3.5 (6c); Ch. 35: Claims-Made Ratemaking (6d); Ch. 36: Individual Risk Rating and Funding Allocation for Self-Insurers, excluding section 36.7 (6e); Ch. 10: A Reinsurance Primer, including the errata for Chapter 10 (7a-c).

Part 1 Introduction

1 About this Textbook

• 1.0 Introduction
• 1.1 Framework for the Textbook
• 1.2 Limitations Associated with All Examples Included in the Textbook
• 1.3 Language and Terminology
• 1.4 Good Practice
• 1.5 Concluding Remarks

2 Key Considerations for GI Actuaries Conducting Actuarial Work

• 2.0 Introduction
• 2.1 Professionalism Requirements
• 2.2 CAS Statement of Principles on Reserving and Ratemaking

Part 2 Key Concepts

3 Ultimate Claims and Expenses

• 3.0 Introduction
• 3.1 What are ultimate claims?
• 3.2 Why are estimates of ultimate values required?
• 3.3 When are projections of ultimate claims prepared?
• 3.4 Who Projects Ultimate Claims?
• 3.5 Concluding Remarks

4 Data

• 4.0 Introduction
• 4.1 Standards and Data
• 4.2 Selection of Data
• 4.3 Homogeneity and Statistical Reliability of Data
• 4.4 Claim Data
• 4.5 Exposure Data
• 4.6 Expense Data
• 4.7 Other Data
• 4.8 Granularity of Data Required
• 4.9 Internal versus External Data
• 4.10 Reliance on Data Supplied by Others
• 4.11 Review of Data
• 4.12 Use of Data
• 4.13 Disclosures and Documentation with Respect to Data Quality
• 4.14 Concluding Remarks

5 Qualitative Information About the Insurer and Its Environment

• 5.0 Introduction
• 5.1 Information Internal to the Organization
• 5.2 Information Required Through Actuarial Standards Specific to Pricing
• 5.3 Information External to the Insurer
• 5.4 Concluding Remarks

6 Credibility

• 6.0 Introduction
• 6.1 Credibility Defined
• 6.2 A General Discussion of Credibility
• 6.3 Relative Nature of Credibility
• 6.4 Considerations for Credibility
• 6.5 The Credibility-Weighting Formula
• 6.6 Traditional Credibility Procedures
• 6.7 Concluding Remarks

7 Trend

• 7.0 Introduction
• 7.1 Standards and Trend
• 7.2 Types of Trend
• 7.3 Trend Differentiated from Claim Development
• 7.4 Good Practices for Trending Procedures
• 7.5 Data Required for Trending Analyses
• 7.6 Concluding Remarks

8 Documentation

• 8.0 Introduction
• 8.1 Documentation for Compliance with Standards
• 8.2 Good Practices for Documentation Procedures
• 8.3 Concluding Remarks

9 Professional Judgment

• 9.0 Introduction
• 9.1 Professional Judgment as Required by Standards
• 9.2 Concluding Remarks

10 A Reinsurance Primer

• 10.0 Importance of Understanding the Effect of Reinsurance
• 10.1 Reinsurance Defined: Insurance for Insurers
• 10.2 Key Reinsurance Terms
• 10.3 Principal Functions of Reinsurance
• 10.4 Types of Reinsurance
• 10.5 Risk-Attaching and Loss-Occurring Reinsurance Contracts
• 10.6 Reinsurance Contract Terms Affecting Actuarial Work
• 10.7 Concluding Remarks

Part 3 Preparing the Data

11 The Development Triangle

• 11.0 Introduction
• 11.1 Key Components of the Development Triangle
• 11.2 Creating a Development Triangle from Calendar Year-end Reports
• 11.3 Creating a Development Triangle from Detailed Claim Transaction Data
• 11.4 Calendar Year Claim Data
• 11.5 Concluding Remarks

12 Earning Exposures

• 12.0 Introduction
• 12.1 Types of Exposures
• 12.2 Written and Earned Premiums for Annual Policies
• 12.3 Written and Earned Premiums for Semi-Annual Policies
• 12.4 Written and Earned Premiums for Multi-Year Policies
• 12.5 Written, Earned, and Unearned Premiums
• 12.6 GI Policies where Exposures are Not Earned Evenly through the Policy Term
• 12.7 Displaying Earned Premium with a Parallelogram
• 12.8 In-Force Premiums

13 Adjusting Premiums for Rate Changes

• 13.0 Introduction
• 13.1 Extension of Exposures Method
• 13.2 Parallelogram Method
• 13.3 Types of Change Influencing Premiums
• 13.4 Developing Premiums to an Ultimate Value
• 13.5 Concluding Remarks

Part 4 Basic Methods for Estimating Ultimate Claims

• General Overview of Part 4
• Detailed Examples in Part 4
• Principles Relevant to the Projection of Ultimate Claims
• Selection of Methods to Use for Projecting Ultimate Claims
  • Considerations for Selecting Methods as Set Out in Standards
  • Requirement for Multiple Methods
  • Considerations for Actuaries Working with Reinsurers
• Good Practice for Projecting Ultimate Claims
  • Good Practice Related to Required Data
  • Good Practice Related to Large Claims
  • Good Practice Related to Analyses of Reinsurance Recoverables
  • Good Practice Related to Comparison of Current Actuarial Work to Prior Actuarial Work
• The Importance of Professional Judgment
• Application of Projection Methods on an Aggregate versus Individual Claim Basis
• Documentation of Key Assumptions and Calculations

14 The Development Triangle as an Investigative Tool

• 14.0 Introduction
• 14.1 The Actuarial Control Cycle
• 14.2 Types of Development Investigative Tests
• 14.3 Auto Insurer, a Detailed Example
• 14.4 Development Diagnostic Analyses for Reinsurers
• 14.5 Concluding Remarks

15 The Development Method

• 15.0 Introduction and General Description of the Development Method
• 15.1 Key Assumptions of the Development Method
• 15.2 The Development Method as Input to Other Projection Methods
• 15.3 General Description of Procedures for the Development Method
• 15.4 Detailed Description of the Development Method – Auto Insurer
• 15.5 Adjustment for Large Claims
• 15.6 Dentist Insurer – Development Method with Ratios and Limited Data
• 15.7 The Development Method and Collision Insurer
• 15.8 The Development Method and Reinsurance

16 Frequency-Severity Methods

• 16.0 Introduction and General Description of Frequency-Severity Methods
• 16.1 Frequency-Severity Methods as Input to Other Projection Methods
• 16.2 Key Assumptions of Frequency-Severity Methods
• 16.3 Two Alternative Approaches for a Frequency-Severity Method
• 16.4 Dentist Insurer
• 16.5 Collision Insurer
• 16.6 Auto Insurer and the Closure Method
• 16.7 Frequency-Severity Methods and Reinsurers

17 The Expected Method

• 17.0 Introduction and General Description of the Expected Method
• 17.1 Key Assumptions of the Expected Method
• 17.2 The Expected Method as Input to Other Projection Methods
• 17.3 Best Exposure Base for Estimating Expected Claims
• 17.4 Description of Procedures for the Expected Method
• 17.5 The Expected Method and Auto Insurer
• 17.6 Dentist Insurer
• 17.7 Collision Insurer
• 17.8 Expected Method and Reinsurers

18 The Bornhuetter Ferguson Method

• 18.0 Introduction and General Description of the Bornhuetter Ferguson Method
• 18.1 Key Assumptions of the Bornhuetter Ferguson Method
• 18.2 The Bornhuetter Ferguson Method as Input to Other Projection Methods
• 18.3 Description of Procedures for the Bornhuetter Ferguson Method
• 18.4 Auto Insurer
• 18.5 The Bornhuetter Ferguson Method and Credibility Weighting
• 18.6 Dentist Insurer
• 18.7 Collision Insurer
• 18.8 The Bornhuetter Ferguson Method and Reinsurers

19 The Cape Cod Method

• 19.0 Introduction and General Description of the Cape Cod Method
• 19.1 Key Assumptions of the Cape Cod Method
• 19.2 Description of Procedures for the Cape Cod Method
• 19.3 Auto Insurer
• 19.4 Dentist Insurer
• 19.5 Collision Insurer
• 19.6 The Cape Cod Method and Reinsurers

20 Berquist-Sherman Adjustments

• 20.0 Introduction and General Description of Berquist-Sherman Adjustments
• 20.1 Key Assumptions of the Berquist-Sherman Adjustments
• 20.2 Berquist-Sherman as Input to Other Projection Methods
• 20.3 Auto Insurer Example Using the Berquist-Sherman Adjustment for Changes in the Adequacy of Case Estimates
• 20.4 Auto Insurer Example Using the Berquist-Sherman Adjustment for Changing Settlement Rates
• 20.5 Auto Insurer Example Using the Berquist-Sherman Adjustments for Changes in Both Case Estimates and Settlement Rates
• 20.6 Berquist-Sherman Adjustments and Actuaries Working with Reinsurance

21 Impact of Changing Conditions on Projection Methods

• 21.0 Introduction
• 21.1 The Importance of Recognizing Changing Conditions in Actuarial Work
• 21.2 Influence of Problems Affecting the Historical Experience
• 21.3 Further Discussion of Changing Conditions
• 21.4 First Example of Changing Conditions – Effect on Projections of Reported and Paid Claims
• 21.5 Second Example – Changing Mix of Business

22 Evaluating and Selecting Estimates Of Ultimate Claims

• 22.0 Introduction
• 22.1 Standards Related to Actuarial Central and Best Estimates
• 22.2 Considerations for Selecting Ultimate Claims
• 22.3 Evaluation of the Projection Methods
• 22.4 Selecting Ultimate Claims for Auto Insurer

Part 5 Financial Reporting

23 Unpaid Unallocated Loss Adjustment Expense

• 23.0 Introduction
• 23.1 Ratio-based Methods
• 23.2 Count-based Method
• 23.3 Unpaid ULAE for Self-Insurers
• 23.4 Unpaid ULAE for Reinsurers

24 Claim Liabilities

• 24.0 Introduction
• 24.1 Estimates of Unpaid Claims
• 24.2 Reserves for Financial Reporting
• 24.3 Claim Liabilities for Auto Insurer

25 Premium Liabilities

• 25.0 Introduction
• 25.1 Premium Liabilities and Standards
• 25.2 Premium Liabilities and an Insurer’s Financial Statements
• 25.3 Common Approaches for Estimating Premium Liabilities
• 25.4 Relative Size of Premium Liabilities
• 25.5 Components of Premium Liabilities based on the Prospective Approach
• 25.6 Calculating Premium Liabilities – An Example
• 25.7 Premium Liabilities and Financial Statements

Part 6 Trending Procedures and Calculating Trend Factors for Claims and Exposures

26 Calculating Trend in Claims

• 26.0 Introduction
• 26.1 Focus on Fundamental Cost Drivers: Frequency and Severity
• 26.2 Influences of Portfolio Changes on Frequency and Severity
• 26.3 Requirement for Homogeneous Data
• 26.4 Trending Procedures
• 26.5 Example with Industry Data – Part 1
• 26.6 Linear and Exponential Regression Analyses
• 26.7 Example with Industry Data – Part 2
• 26.8 Combining Experience from Different Sources for Trending Procedures
• 26.9 Trend and Time Periods
• 26.10 Development Factors and Trend Factors – Overlap Fallacy
• 26.11 Concluding Remarks

27 Calculating Exposure and Premium Trend

• 27.0 Introduction
• 27.1 Inflation-Sensitive Exposures
• 27.2 Changes in the Mix of Exposures
• 27.3 Time Periods for Premium Trend
• 27.4 Premium Trend Examples
• 27.5 Concluding Remarks

Part 7 Ratemaking

• Actuaries and GI Pricing
• The Actuarial Control Cycle
• Risks in GI Pricing
• GI Pricing and Regulation
• The Premium Equation
• Outline of Part 7

28 Rate Regulation

• 28.0 Introduction
• 28.1 Objectives of GI Rate Regulation
• 28.2 The Rate Regulation Continuum
• 28.3 Description of Rate Regulatory Approaches
• 28.4 Concluding Remarks

29 Manual Ratemaking

• 29.0 Introduction
• 29.1 Manual Rating
• 29.2 The Rating Manual
• 29.3 Rating Rules
• 29.4 Rating Algorithm
• 29.5 Rate Pages
• 29.6 Discounts and Surcharges
• 29.7 The Role of Actuaries in Manual Rating
• 29.8 Concluding Remarks

30 Expenses and Profit and Contingencies

• 30.0 Introduction
• 30.1 Expenses and Standards
• 30.2 Expenses and Regulatory Requirements
• 30.3 Types of Expenses Defined
• 30.4 Variable versus Fixed Expenses
• 30.5 Considerations for the Actuary for Expense Analysis
• 30.6 Quantifying Specific Types of Expenses
• 30.7 Allocation of Expenses to Coverages for Automobile Insurance
• 30.8 Reinsurance Expenses
• 30.9 Profit and Contingencies
• 30.10 Concluding Remarks

31 Catastrophes and Large Claims

• 31.0 Introduction
• 31.1 Declaring an Event a Catastrophe
• 31.2 The Most Common Catastrophes Affecting GI
• 31.3 Large Claims
• 31.4 Loadings for Catastrophes and Large Claims in GI Ratemaking
• 31.5 Catastrophe Loadings in GI Ratemaking and Standards
• 31.6 Catastrophe Loadings for Homeowners Insurer
• 31.7 Loading for Large Claims for Homeowners Insurer
• 31.8 Concluding Remarks

32 Basic GI Ratemaking Approaches

• 32.0 Introduction
• 32.1 Notation
• 32.2 Pure Premium Approach
• 32.3 Claim Ratio Approach
• 32.4 The Ratemaking Formulas and the Basic Equation for an Insurer’s Premiums
• 32.5 Auto Insurer as an Example of the Equivalence of the Pure Premium and Claim Ratio Approaches
• 32.6 Use of the Pure Premium Versus Claim Ratio Approach
• 32.7 Classical Credibility Approach as Input to Ratemaking Analysis
• 32.8 Credibility and Calculating the Indicated Rate or Indicated Rate Change
• 32.9 The Pure Premium Approach Applied to Dentist Insurer
• 32.10 The Claim Ratio Approach Applied to Collision Insurer
• 32.11 The Claim Ratio Approach for Homeowners Insurer
• 32.12 Weights Assigned to Years in the Experience Period
• 32.13 Concluding Remarks

33 Basic GI Risk Classification

• 33.0 Introduction
• 33.1 Purpose of Risk Classification
• 33.2 Three Parts to Development of Risk Classification Systems
• 33.3 Risk Characteristics
• 33.4 Risk Classes
• 33.5 Risk Classification Systems
• 33.6 Risk Classification Using a Single Variable
• 33.7 Risk Classification Using Multiple Variables
• 33.8 Territory Risk Classification
• 33.9 Concluding Remarks

34 Actuarial Pricing for Deductibles and Increased Limits

• 34.0 Introduction
• 34.1 Deductibles
• 34.2 Self-Insured Retention versus Large Deductible
• 34.3 Coinsurance
• 34.4 Policy Limits
• 34.5 Data Sources for Calculating Deductible Factors and ILFs
• 34.6 Challenges with Empirical Data for Calculating Deductible Factors and ILFs
• 34.7 Using Statistical Distributions to Determine Deductible Factors and ILFs
• 34.8 Self-Insured Municipality – an Example with Empirical Data for GL
• 34.9 Example with Industry Aggregated Claim Data
• 34.10 Censored Data – Deductible and ILF Analyses
• 34.11 Consistency Testing and Other Considerations
• 34.12 Concluding Remarks

35 Claims-Made Ratemaking

• 35.0 Introduction
• 35.1 History of Claims-Made Coverage
• 35.2 Understanding Claims-Made Coverage with the Accident Year Lag by Report Year Matrix
• 35.3 Principles of Claims-Made Ratemaking
• 35.4 Determining Rates for Claims-Made Policies Using the Marker and Mohl Accident Year Lag by Report Year Matrix
• 35.5 Current Approaches for Claims-Made Ratemaking
• 35.6 Coordinating Changes in Claims-Made Insurance
• 35.7 Concluding Remarks

36 Individual Risk Rating and Funding Allocation for Self-Insurers

• 36.0 Introduction
• 36.1 Introduction to Individual Risk Rating for Insurers and Self-Insurers
• 36.2 Schedule Rating and Judgment Rating
• 36.3 Prospective Experience Rating
• 36.4 Retrospective Rating
• 36.5 Dividend Plans and Safety Groups
• 36.6 Comparison of Individual Risk Rating Programs
• 36.7 Funding Allocation for Self-Insurers
• 36.8 Concluding Remarks

Part 8 Monitoring Results

37 Monitoring Results

• 37.0 Introduction
• 37.1 Monitoring
• 37.2 Methods for Monitoring Claims
• 37.3 Comparison of Actual to Expected Claims for Dentist Insurer
• 37.4 Key Decisions for Actuaries in Selecting a Development Pattern for Comparison of Actual to Expected Claims
• 37.5 Comparison of Actual to Expected Claims for Public Entity Self-Insurance Pool
• 37.6 Options for Interpolation of Development Patterns
• 37.7 Monitoring Activities Specific to Ratemaking
• 37.8 Concluding Remarks

References

Glossary

Commonly Used Abbreviations

Index

Appendices A through F: Case Studies

• Appendix A: Dentist Insurer
• Appendix D: ABC Manufacturing Company/ABCMC Captive
• Appendix E: Public Entity Self-Insurance Pool

Appendix G Development Analysis for Excess Limits and Layers

Appendix H Appointed Actuary’s Questionnaire

Sources

• Fundamentals of General Insurance Actuarial Analysis, Second Edition, Volume I, sample pages (SOA / ACTEX Mad River Books) — the document: title page, copyright page (ISBN 978-0-99133-632-6, copyright 2022 Society of Actuaries), the printed contents with every chapter and section heading, the bookmark outline for Part 1 to Chapter 22, and Chapter 1's description of the book's structure (sha256 ff4114fa5b0ad0800fabf09cf68578882df97ac1c4d04988ea562d5c8771000f); the sample's contents do not print titles for Appendices B, C and F
• FSA Exam Book List, Nov 2026 / Mar 2027 / Jul 2027 (SOA) — the edition, year, publisher and ISBN (978-0-9913363-2-6) for GI 101 and GI 201
• GI 101 Ratemaking and Reserving syllabus, Nov 2026 / Mar 2027 / Jul 2027 (SOA) — the citation and the assigned parts, chapters and exclusions
• GI 201 syllabus, Nov 2026 / Mar 2027 (SOA) — the assigned chapters
• GI 301 syllabus, Mar 2027 / Jul 2027 (SOA) — the assigned chapters, appendices and sections, and the titles of Appendices A, D, E and G